Is Jayce the worst character in the game?

I have been using Jayce a fair bit since purchasing him. I have played almost every champ in the game, and have a strong versatility in the majority of them; I however find Jayce to be such a niche pick that he is almost useless.

He can't melee worth a damn, and he has pretty bad damage when in range mode. Q is practically useless outside of his E gateway. Using the gateway makes it abundantly clear where his shot is going / coming from, and although the shot looks big, the hitbox is abyssal. Blitz and Thresh's hook have a wider hit box than Q combined with his E, as does Olafs axe.

He is extremely mana dependant, forcing you to buy tear early on, hurting your early game damage even more when other lanes are stacking armor, MR, AP, or AD to compensate, pushing his laning further back in the early game. The fact that you need to line up two abilities to do good damage really drains that mana. It's also a horrible feeling when you miss, considering it has a 16 second cooldown, and together you are looking at a MINIMUM of 105 mana at level 1 for both.

In hammer stance, his attack damage is also quite low. You can't build attack speed on him, as this takes away entirely from his Q/E combo. You have to burst, HOPE you kill them.....and then sit on painstakingly long cooldown times. He is one of the only champs in the game where you are forced to buy Lucidity boots simply for the CDR.

Am I missing something with Jayce? He feels like a really REALLY bad version of Nidalee. With Nid you need to land just 1 skill shot, which does roughly the same damage as Jayce's Q when combined with E. Nid can heal herself, and doesn't have to worry about mana issues when in cat form. She also has a much better escape and burst mechanism.

Am I missing anything else with Jayce? Anyone else think he deserves a bit of an upgrade?